Presenter Keys resigned and pundit Gray was sacked by Sky last month in the aftermath of their off-air sexist comments about female assistant referee Sian Massey.
According to The Guardian, the pair will present a three-hour show between 10am and 1pm every weekday, beginning this Monday, February 14.
Keys said: "We are delighted to be joining the TalkSport family and can't wait to get started."
He added that the show was the "start of something new and very exciting for Andy and myself".
Gray said: "I can't tell you how excited I am to be joining TalkSport. It's a wonderful opportunity for Richard and I to do what we do best and that's talk about sport."
TalkSport programme director Moz Dee added: "The events of the last couple of weeks have been a lesson and has changed them.
"One thing that hasn't changed however is that they are two iconic broadcasters who have a wealth of experience in the world of sport and that's what we have to do now - move forward with them as sports broadcasters.
"I think it's a sensational coup for TalkSport and great for radio. These men have carved out amazing careers in television and were at the forefront of the Sky revolution. I think they are going to have a massive impact on the radio scene."